Remark 55 Our primary interest is the case where \(\Omega \subset \mathbb {R}^2\)  is a rectangular domain and it is partitioned by the uniform triangulation mesh. For other cases such as \(\Omega \)  is not rectangular, the mesh is not uniform, or the deep CNN is not trained based on raster images, the mapping \(\mathcal {M}\) 
should be redefined. For the case where \(\Omega \subset \mathbb {R}^3\) , one may employ a
deep 3D CNN (see, e.g., [1]}). These much more complicated situations should be discussed case by case with significantly more techniques, and they are beyond the scope of this paper.

